THE WIFE OF BEITH is a long poem, not meant to be sung, I don't think, although maybe someone could construct a song from it. It was first published anonymously as a chapbook, in the 18th century in Glasgow. It was reprinted in John Cheap, the Chapman's Library: The Scottish Chap Literature of Last Century Classified, 1877. The opening lines make it clear that the character is based on Chaucer's WIFE OF BATH (or perhaps both WIFE OF BATH and WIFE OF BEITH are based on the same older tales):

IN Beith once dwelt a worthy wife,
Of whom brave Chaucer mention makes
She lived a licentious life,
And namely in venereal acts
But death did come for all her cracks;
When years were spent and days out driven.
Then suddenly she sickness takes,
Deceased forthwith, and went to heaven.
But as she went upon the way,
There followed her a certain guide…

The guide, of course, turns out to be the devil, who leads her to hell instead, but she escapes, in a story reminiscent of THE DEVIL AND THE FARMER'S WIFE and all its variations.